a-permanent-manned-space-colony-at-eml1-earth-moon-lagrange-point-1

This project attempts to determine whether or not use of a "Gravity Winch" can add L1 to the list of practical habitation locations in near-Earth space such as L4, L5, and Earth's Moon. The Gravity Winch is a concept that utilizes the purposeful movement of "Gravity Anchors" as a means of shifting or maintaining a position in space. L1 is uniquely suited to the use of a Gravity Winch, since it possesses two gravity wells down which Gravity Anchors may be lowered.
email contact: Joseph Bland, [email protected]

How is this relevant to the Challenge of creating an Asteroid Mission? It turns out that EML1 is one of the best places from which to launch a mission to an asteroid. So creating a stable platform at L1 will be very important to many future Asteroid Missions.

The Gravity Winch is a concept that
utilizes the purposeful movement of "Gravity Anchors" as a means of
shifting or maintaining a position in space. L1 is uniquely suited to the use
of a Gravity Winch, since it possesses two gravity wells down which Gravity
Anchors may be lowered Sacramento L5 Society, local California chapter of
the National Space Society, has been engaged over the last year in
analyzing possible means for powering a Moon base through the two week
long lunar night. One of the attractive means for accomplishing this appears
to be the creation of a solar-powered laser platform based at EML1
(Earth-Moon Lagrange point 1). However, a NASA 2009 concept study
( http://www.nasa.gov/pdf/315858main_Cheng-yi_Lu.pdf ) suggests that a
very large percentage of the total system mass of such a laser system would
be composed of the apparatus necessary for "station-keeping" at L1. Further,
the fuel for station-keeping would need to be continually replenished over time.

It was while exploring alternative station-keeping means that the idea of the

Gravity Winch came into being. The Gravity Winch is a concept that utilizes the
purposeful movement of Gravity Anchors as a means of shifting or maintaining
a platform's position at L1. A Gravity Anchor is simply a line or "tether" dropped
down a gravity well, augmented with a mass at the end of the tether. L1 is uniquely
suited to the use of a Gravity Winch, since it possesses two gravity wells down
which Gravity Anchors may be lowered.

In function, a tether is dropped down both the Moon’s gravity well and Earth’s.

Such an arrangement could be composed either of two separate tethers, each
with their own Gravity Winch, or it can be composed of a single tether sharing a
single Gravity Winch. In the case of the single tether approach, lifting one Gravity
Anchor out of one gravity well is matched by dropping the other Gravity Anchor
down the other gravity well. (Note: For the time being, further analysis will be
confined to studying the single tether approach at L1.)

There are long term and short term effects involved with the use of a Gravity

Winch. Long term, moving the Gravity Anchors with the Gravity Winch increases
or decreases the pull of gravity from one direction or the other by increasing or
decreasing the relative pull of gravity on the weighted end. That is, when a weighted
tether is deeper in one of the gravity wells, it is at the same time shallower in the
other gravity well. That creates a net increase in pull towards the gravity well the
weight is deeper in. And since gravity continually acts, the pull is additive over time.

Short term, it seems intuitively clear that, with careful shifting of the Gravity Anchors

from one side to the other, the L1-based platform is able to be “balanced” between the
two gravity wells, similar to the way a long pole helps a tightrope walker to balance.

In terms of station-keeping, both these effects can be thought of as removing the

“z” vector (along the Earth-Moon axis) from fuel-burning station-keeping consideration,
thus allowing fuel-burning station-keeping to concentrate on the “x" and “y” vectors. That
alone is a useful aspect of a Gravity Winch, and should be a real aid in reducing station-
keeping requirements. Most importantly, a Gravity Winch allows the L1-based platform to
be continually shifted in the z axis, without expending fuel, as the Moon (and the L1 point)
moves farther from and closer to the Earth in throughout the Moon's elliptical orbit. Note
that this continual movement of the L1-based platform may be accomplished without the
need for expending fuel of any sort, although work, provided by a solar energy converter,
will need to be expended via the Gravity Winch itself.

It is clear, therefore, that a Gravity Winch should be able to maintain station keeping

along the z axis. Interestingly, though, it may be that a Gravity Winch can also help to maintain
station keeping along the x and y axes as well. Consider that two Gravity Anchors in effect
place a tension on the connecting tether, and that at the approximate middle of that tether sits
the platform being stabilized at L1. That tension connects the two weighted ends in a straight
line pointed at the exact center of gravity of the Earth and the Moon. And any movement of a
portion of the tether, as by an attached station moving in the x and/or y vectors, is thus countered
by the force of opposing gravities that wants to keep the tether straight. Thus, a Gravity Winch
may be able to keep the L1-based platform from "drifting away" in all three axes, thus obviating
the need for any other form of fuel-burning station keeping other than the Gravity Winch itself.

There is one more interesting potential use of a Gravity Winch at L1. It may also be considered

to represent the starting tether of an eventual “lunar space elevator”. By lengthening the tethers
in both directions over time, eventually the Moon side tether can be made to touch down directly
on the lunar surface.

Proof of concept prototype:
1. Set a pole (pole #1) on a stand.
2. Attach pole #1 to the stand with a hinge so that it can fall left or right but not front or back.
3. Attach a second pole (pole #2) to the first at right angles (a cross shape).
4. Pole #2 would be attached through a linear motor that could move pole #2 left or right on pole #1.
5. Attach a means of sensing what the angle left or right of pole #1 is, as by putting a sensor at the hinge area.
6. Attach a means of sensing what the position left or right of pole # 2 is, as by putting a sensor on the linear motor.
7. At each degree (or fraction of a degree) of "falling" movement of pole #1 and #2, calculate the force moving the poles towards falling. Note that this force changes as the pole(s) fall farther and farther over.
8. Calculate the required opposing movement of pole #2 required to stop the "falling" movement of pole #2.
A. Movement of pole #2 will itself impart a force to the "falling" movement of pole #1, because pole #2 receives a momentum when it is moved by the linear motor (pole #1 wants to move in the opposite direction of pole #2). Since pole #2 needs to move left when pole #1 is "falling" right (in order to balance the "weight"), then this force of momentum adds to the force pushing pole #1 over. That force needs to be calculated as well and added to the "countering" force of pole #2.
B. The momentum pole #2 receives when it is moved by the linear motor is "recovered" when pole #2 stops moving (particularly if these movements are abrupt). That force needs to be calculated as well and subtracted from the "countering" force of pole #2. Note: Apart from the friction, the momentum imparted when pole #2 is moved should equal the momentum regained when pole #2 is stopped. However, since the poles are "falling", the acceleration given the falling poles cannot be totally cancelled. That's what makes the calculation tricky!
9. Calculate the required movement of pole #1 to return it to "balance", that is, neither falling left or right. See step number 8 above for additional elements of the calculation.
10. Return pole #2 to its centered position.

“The Earth, The Moon, and EML1”
a “Hi, folks, my name is Joe Bland, and I’m the President of the Sacramento, California chapter of the National Space Society. This is a little play I’ve written to explain the idea of the Gravity Winch.
So here we have the big, burly Earth, as represented for us by __. And here we have the petite, delicate Moon, as represented by ____. This rope represent the gravity between the Earth and the Moon. At about four/fifths of the distance from the Earth to the Moon, the Moon’s gravity attracts exactly the same amount as the Earth’s gravity. We call that point in space Earth-Moon Lagrange Point 1, or EML1 for short. Representing EML1 for us is __.”

(EML1 always holds onto one spot on the rope and will move as the Moon moves.)

“Playing the part of the Earth Gravity Anchor is _____________, and playing the part of the Moon Gravity Anchor is ______________. Playing the part of a Space Station is me. This second rope will represent the tether that connects the Space Station and the two Anchors together. My hands will represent the Gravity Winch. ”

(The two Anchors and the Space Station hold a second rope.)

“We’ve arranged that, at EML1, the two Anchors and the Space Station are equally attracted by the Earth and the Moon. But this is a very delicate balancing act. For one thing, the Moon doesn’t make a perfect circle around the Earth. Instead, it makes an ellipse. That means the Moon moves farther from the Earth for half its orbit, and closer to the Earth for the other half. And the EML1 point does the same. Until now, to keep an object like a Space Station at EML1, we’ve had to continually move the Space Station with rockets.”

(The Space Station “blows” himself and the Anchors to EML1. Then everyone stops and returns to the original position.)

“But it turns out we may be able to move the Space Station with gravity itself. Let’s say the Moon starts moving away from the Earth.”

(The Moon and EML1 slowly move a little away from the Earth.)

“Right away, the force of gravity from the Moon starts to weaken, and as a result the Space Station and the Space Anchors start to fall towards the Earth.”

(The Space Station and the Space Anchors even more slowly move towards the Earth.)

“Immediately, the Space Station uses its Gravity Winch to reel in the Earth Gravity Anchor and let out the Moon Gravity Anchor, moving both Anchors towards the Moon and away from the Earth.”

(The Gravity Winch moves the rope and the Anchors towards the Moon and EML1, which are still slowly moving away.)

“Now, because of a law of physics called action/reaction, moving the Space Anchors towards the Moon means that the Space Station is also moved towards the Earth.”

(The Space Station moves a little more towards the Earth. The rope and the space anchors continue to be moved towards the Moon by the Gravity Winch, while the Moon and EML1 continue to move slowly away.)

“But fortunately, the Space Station is a LOT bigger than the two space anchors, so it doesn’t move very far away from EML1 at all. Meanwhile, the Space Station can move the Gravity Anchors a whole bunch. Pretty soon, the Moon is a lot closer to the Anchors than it was, and the Earth is a lot farther away. So the force of the Moon’s gravity on the Anchors has been increased while the force of the Earth’s gravity has been reduced. As a result, the Space Station, just grabbing onto the tether between the two Anchors, stops falling towards the Earth, and starts falling back towards the Moon.”

(The Space Station starts moving towards L1 and the Moon, while the rope and the Anchors slow down to move at the same speed as the Space Station.)

“Thus, we have managed to move the Space Station to follow the EML1 point - without using any rocket power. That doesn’t mean, by the way, that we didn’t use any energy. We had to power our Gravity Winch with energy. But we can get this energy directly from the sun with solar cells, which means we don’t need to continually bring up fuel to our Space Station with a rocket. And that’s the advantage of the Gravity Winch.
Take a bow, everyone!”

Finally, if we have a few more seconds, I’d like to have everyone help me with a little experiment. So stand up. Now stand on your tippy-toes. Now slowly start to move your right arm forward and your left arm back. Now slowly reverse the arms. Now move your arms back and forward faster and try to stay on your toes. Alright, stop and relax. This time, stand on tippy toes, then slowly move both arms forward, then slowly backward. Now move them back and forward faster and faster, and try to stay on your toes.What just happened is gravity unbalancing you. That is exactly the same force that would make the Gravity Winch work. A real-world example of this in action is a Segway transporter (Figure 1).
Questions?”Figure 1

Demonstrator prototype:

Attach a pole (pole #1) to a stand with a hinge so that it can fall left or right but
not front or back.

Attach a second pole (pole #2) to the first at right angles (a cross shape).
Pole #2 would be attached with a linear bearing (very low friction preferred) that
would let pole #2 move left or right on pole #1.

Mark angles on a protractor at the hinge point of pole #1.

Mark distances from the midpoint right and left on pole #2.
To calibrate:

Move pole #1 one degree to the left of the balance point

Move pole #2 sufficiently to the rigtht to "balance" the pole. Note the
distance required.

Move pole #1 one degree to the right of the balance point

Move pole #2 sufficiently to the left to "balance" th pole. Note the
distance required.

Continue this process advance one degree until the pole cannot move
to balance. Note the distances required.
To test:

Attach a string to each end of pole #2.

Hook each string through a pulley so that both strings can be held by
the operator, one in each hand.